Hi
On 13 Mar 2001, dennis roberts wrote:
> i give a survey and ... have categorized respondents into male and females
> ... and also into science major and non science majors ... and find a data
> table like:
> non science science
> C1 C2 Total
> M 1 24 43 67
> 32.98 34.02
>
> F 2 39 22 61
> 30.02 30.98
>
> Total 63 65 128
>
> Chi-Sq = 2.444 + 2.368 +
> 2.684 + 2.601 = 10.097
> DF = 1, P-Value = 0.001
>
> when we evaluate THIS test ... with the chi square test statistic we use in
> THIS case ... in what sense would this be considered to be a TWO tailed
> test?
In the sense that Chi^2 would give you the same value if your
cells had been 43 24 for Males and 22 39 for females (i.e., the
reverse direction of relationship between gender and
science). This is most easily demonstrated by calculating the
z-test equivalent to your chi^2 test.
z = (.6418-.3607)/[sqrt{.5078*.4922( (1/67) + (1/61))}]
= .2811 / .08847
= 3.1772
z^2 = chi^2
The p-value for z that corresponds to the chi^2 p-value is
p(z<= -3.1772 or z>= +3.1772) i.e., a "two-tailed" probability
If the proportions were reversed, z would become negative. This
makes it easier to see that there are directional (i.e.,
"one-tailed") and non-directional (i.e., "two-tailed") hypotheses
being tested by the chi^2.
The chi^2 distribution is equivalent to the z distribution
"folded over" so that both negative and positive tails of z are
in the upper (i.e., positive) tail of chi^2. The same
relationship holds between t and F. As we saw recently on this
(or another stats list), there is much confusion between
"one-tailed" in the sense of a directional test (which concerns
the direction of differences or correlations) and "one-tailed" in
the narrower sense of tail of distribution (e.g., chi^2). These
uses are _not_ equivalent. Perhaps less confusing if we use
"directional" or some other term besides "one-tailed" for the
first sense.
Best wishes
Jim
============================================================================
James M. Clark (204) 786-9757
Department of Psychology (204) 774-4134 Fax
University of Winnipeg 4L05D
Winnipeg, Manitoba R3B 2E9 [EMAIL PROTECTED]
CANADA http://www.uwinnipeg.ca/~clark
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